Our peer-reviewed Journal of Free Speech Law, which is now two years old, has published over fifty articles, including by Jack Balkin (Yale), Mark Lemley (Stanford), Jeremy Waldron (NYU), Cynthia Estlund (NYU, forthcoming within a week or so), Christopher Yoo (Penn), Danielle Citron (Virginia), and many others—both prominent figures in the field and emerging young scholars (including ones who didn't have a tenure-track academic appointment).
I expect that many authors are planning to submit articles on free speech to the usual law reviews when the submission cycle restarts in August. But if you submit exclusively to us before that, we will give you an answer within 14 days (our guarantee, which we have so far never broken); and then if you'd like to have it published quickly, we can publish it in within several weeks, if it's sufficiently clean and cite-checked by your research assistant. (We can also have it cite-checked for you by one of our student staffers, but that takes a bit longer.) This means your article can be published by us, if it's accepted, almost a year (or more) before it would be published by the law journals.
Of course, also please pass this along to friends or colleagues who you think might be interested. Note that the submissions don't compete for a limited number of slots in an issue or volume; we'll publish articles that satisfy our quality standards whenever we get them.